#883574 (Rust) No.2170 Left Addition Machine

• 問題: No.2170 Left Addition Machine
• ユーザー: koba-e964
• 提出日時: 2023-06-23 01:28:06
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 204 ms / 2,000 ms
• コード長: 7,327 bytes
• コンパイル時間: 7,182 ms
• コンパイル使用メモリ: 162,812 KB
• 実行使用メモリ: 41,068 KB
• 最終ジャッジ日時: 2023-09-12 19:38:26
• 合計ジャッジ時間: 23,997 ms
• ジャッジサーバーID （参考情報）: judge14 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 4,380 KB
testcase_01	AC	1 ms; 4,380 KB
testcase_02	AC	2 ms; 4,384 KB
testcase_03	AC	174 ms; 39,092 KB
testcase_04	AC	40 ms; 4,828 KB
testcase_05	AC	92 ms; 18,824 KB
testcase_06	AC	109 ms; 25,668 KB
testcase_07	AC	147 ms; 28,304 KB
testcase_08	AC	40 ms; 16,164 KB
testcase_09	AC	87 ms; 11,436 KB
testcase_10	AC	12 ms; 4,384 KB
testcase_11	AC	81 ms; 21,224 KB
testcase_12	AC	194 ms; 40,968 KB
testcase_13	AC	188 ms; 40,948 KB
testcase_14	AC	189 ms; 40,964 KB
testcase_15	AC	192 ms; 41,028 KB
testcase_16	AC	190 ms; 41,000 KB
testcase_17	AC	187 ms; 40,972 KB
testcase_18	AC	186 ms; 40,976 KB
testcase_19	AC	184 ms; 41,012 KB
testcase_20	AC	192 ms; 41,012 KB
testcase_21	AC	56 ms; 5,040 KB
testcase_22	AC	55 ms; 5,040 KB
testcase_23	AC	56 ms; 5,100 KB
testcase_24	AC	57 ms; 5,096 KB
testcase_25	AC	56 ms; 5,032 KB
testcase_26	AC	56 ms; 5,116 KB
testcase_27	AC	55 ms; 5,056 KB
testcase_28	AC	56 ms; 5,056 KB
testcase_29	AC	56 ms; 5,024 KB
testcase_30	AC	179 ms; 41,004 KB
testcase_31	AC	180 ms; 40,964 KB
testcase_32	AC	179 ms; 41,068 KB
testcase_33	AC	180 ms; 41,032 KB
testcase_34	AC	179 ms; 41,040 KB
testcase_35	AC	183 ms; 41,004 KB
testcase_36	AC	181 ms; 41,024 KB
testcase_37	AC	180 ms; 41,056 KB
testcase_38	AC	182 ms; 41,032 KB
testcase_39	AC	55 ms; 5,048 KB
testcase_40	AC	55 ms; 4,952 KB
testcase_41	AC	57 ms; 5,040 KB
testcase_42	AC	54 ms; 4,956 KB
testcase_43	AC	55 ms; 5,028 KB
testcase_44	AC	55 ms; 5,072 KB
testcase_45	AC	55 ms; 5,044 KB
testcase_46	AC	55 ms; 5,060 KB
testcase_47	AC	55 ms; 5,032 KB
testcase_48	AC	192 ms; 40,956 KB
testcase_49	AC	204 ms; 41,068 KB
testcase_50	AC	196 ms; 41,040 KB
testcase_51	AC	187 ms; 41,056 KB
testcase_52	AC	186 ms; 41,036 KB
testcase_53	AC	191 ms; 41,008 KB
testcase_54	AC	185 ms; 41,052 KB
testcase_55	AC	186 ms; 40,996 KB
testcase_56	AC	185 ms; 41,060 KB
testcase_57	AC	188 ms; 40,968 KB
testcase_58	AC	192 ms; 40,940 KB
testcase_59	AC	191 ms; 40,904 KB
testcase_60	AC	194 ms; 41,028 KB
testcase_61	AC	193 ms; 40,860 KB
testcase_62	AC	192 ms; 40,936 KB
testcase_63	AC	186 ms; 41,032 KB
testcase_64	AC	192 ms; 41,008 KB
testcase_65	AC	188 ms; 40,904 KB
testcase_66	AC	18 ms; 4,388 KB
testcase_67	AC	150 ms; 40,932 KB
testcase_68	AC	187 ms; 41,012 KB

ソースコード

use std::cmp::*;
use std::io::{Write, BufWriter};
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes.by_ref().map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr,) => {};
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) };
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, usize1) => (read_value!($next, usize) - 1);
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
mod mod_int {
    use std::ops::*;
    pub trait Mod: Copy { fn m() -> i64; }
    #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
    impl<M: Mod> ModInt<M> {
        // x >= 0
        pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }
        fn new_internal(x: i64) -> Self {
            ModInt { x: x, phantom: ::std::marker::PhantomData }
        }
        pub fn pow(self, mut e: i64) -> Self {
            debug_assert!(e >= 0);
            let mut sum = ModInt::new_internal(1);
            let mut cur = self;
            while e > 0 {
                if e % 2 != 0 { sum *= cur; }
                cur *= cur;
                e /= 2;
            }
            sum
        }
        #[allow(dead_code)]
        pub fn inv(self) -> Self { self.pow(M::m() - 2) }
    }
    impl<M: Mod> Default for ModInt<M> {
        fn default() -> Self { Self::new_internal(0) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
        type Output = Self;
        fn add(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x + other.x;
            if sum >= M::m() { sum -= M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
        type Output = Self;
        fn sub(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x - other.x;
            if sum < 0 { sum += M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, other: T) { *self = *self + other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, other: T) { *self = *self - other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, other: T) { *self = *self * other; }
    }
    impl<M: Mod> Neg for ModInt<M> {
        type Output = Self;
        fn neg(self) -> Self { ModInt::new(0) - self }
    }
    impl<M> ::std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
} // mod mod_int

macro_rules! define_mod {
    ($struct_name: ident, $modulo: expr) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
        struct $struct_name {}
        impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
    }
}
const MOD: i64 = 998_244_353;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;

// Sparse Table.
// BiOp should be the type of a binary operator which is
// associative, commutative and idempotent.
// (For example, both min and gcd satisfy these properties.)
// Verified by: yukicoder No. 2171
// (https://yukicoder.me/submissions/883410)
struct SparseTable<T, BiOp> {
    biop: BiOp,
    st: Vec<Vec<T>>,
}

impl<T, BiOp> SparseTable<T, BiOp>
    where BiOp: Fn(T, T) -> T,
          T: Copy {
    pub fn new(ary: &[T], biop: BiOp) -> Self {
        let n = ary.len();
        let mut h = 1;
        while 1 << h < n {
            h += 1;
        }
        let mut st: Vec<Vec<T>> = vec![Vec::from(ary); h + 1];
        for i in 0 .. n {
            st[0][i] = ary[i];
        }
        for b in 1 .. (h + 1) {
            if n + 1 < 1 << b {
                break;
            }
            for i in 0 .. (n + 1 - (1 << b)) {
                let next_idx = (1 << (b - 1)) + i;
                st[b][i] = biop(st[b - 1][i], st[b - 1][next_idx]);
            }
        }
        SparseTable {biop: biop, st: st}
    }
    fn top_bit(t: usize) -> usize {
        8 * std::mem::size_of::<usize>() - 1 - t.leading_zeros() as usize
    }
    pub fn query(&self, range: std::ops::Range<usize>) -> T {
        let (f, s) = (range.start, range.end - 1);
        assert!(f <= s);
        let b = Self::top_bit(s + 1 - f);
        let endpoint = s + 1 - (1 << b);
        (self.biop)(self.st[b][f], self.st[b][endpoint])
    }
}

// https://yukicoder.me/problems/no/2170 (3.5)
// elim[i] := max(0, max{x+1 | A[x] <= A[i]}) とする。
// 最終的に選ばれる値としては一番右以外はすべて途中で消えてしまうので、最終的な結果には寄与しない。
// そのため、[L, R) の代わりに [max(L, elim[R- 1]), R) を考えることができる。
// 一番右の要素を選んだら部分問題を解くことになる。j 回再帰するのであれば A[R-1] の寄与は 2^{j} である。
// 最後に残る要素から右に見ていった時、寄与は 1, 1, 2, 4, ..., 2^{x} という列になる。
fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    input! {
        n: usize, q: usize,
        a: [i64; n],
        lr: [(usize1, usize); q],
    }
    let mut pw = vec![MInt::new(0); n + 1];
    pw[0] += 1;
    for i in 1..n + 1 {
        pw[i] = pw[i - 1] * 2;
    }
    let mut acc = vec![MInt::new(0); n + 1];
    for i in (0..n).rev() {
        acc[i] = acc[i + 1] * 2 + a[i];
    }
    let mut st = vec![];
    let mut elim = vec![0; n];
    for i in (0..n).rev() {
        while let Some((val, idx)) = st.pop() {
            if val <= a[i] {
                elim[idx] = i + 1;
                continue;
            } else {
                st.push((val, idx));
                break;
            }
        }
        st.push((a[i], i));
    }
    for (_, idx) in st {
        elim[idx] = 0;
    }
    let spt = SparseTable::new(&elim, max);
    for (l, r) in lr {
        let idx = max(l, spt.query(l..r));
        puts!("{}\n", acc[idx + 1] - acc[r] * pw[r - idx - 1] + a[idx]);
    }
}